Root Protection Area
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BS5837:2012 defines Root Protection Area radius as stem diameter (measured at 1.5m above ground, not the 1.3m DBH convention used elsewhere) converted to metres and multiplied by 12:

RPA radius (m) = stem diameter (m) × 12
RPA area (m²) = π × radius²

Worked example — single stem: a 500mm stem diameter converts to 0.5m, multiplied by 12 gives a 6.0m radius. Area is π × 6² ≈ 113.1m².

Multi-stem trees don't run the formula per stem or use an average — BS5837 uses an aggregate diameter, the square root of the sum of each stem diameter squared, then applies the same 12× multiplier to that one figure:

Aggregate diameter = √(d₁² + d₂² + d₃² + ...)

Worked example — multi-stem: three stems at 200mm, 150mm, and 100mm give an aggregate diameter of √(200² + 150² + 100²) ≈ 269mm — not 450mm (the simple sum) or 150mm (the average). That 269mm aggregate then goes through the same ×12 formula: a 3.23m radius, roughly 32.8m².

The standard caps the calculated area at 707m² per tree (equivalent to a 15m radius) unless specific arboricultural justification supports going larger — this only bites on very large, old single-stem specimens (diameter above roughly 1.25m).